A357305 Numbers k > 1 such that the ratio (numbers of zeros)/(total length) in the binary representation of k^2 is a new minimum.

2, 3, 5, 11, 45, 181, 48589783221, 66537313397, 398064946368587, 796095014224053

Offset: 1

Author

Hugo Pfoertner, Oct 01 2022

Keywords

• nonn
• base
• hard
• more

Examples

			    k    k^2  (binary zeros)/A070939(k^2)
    .      .   .     k^2 written in binary
    2      4  2/3   [1, 0, 0]
    3      9  1/2   [1, 0, 0, 1]
    5     25  2/5   [1, 1, 0, 0, 1]
   11    121  2/7   [1, 1, 1, 1, 0, 0, 1]
   45   2025  3/11  [1, 1, 1, 1, 1, 1, 0, 1, 0, 0, 1]
  181  32761  2/15  [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 1]
		

Crossrefs

Cf. A000120, A000290, A070939, A159918, A230097.

Extensions

a(7)-a(8) from Michael S. Branicky, Oct 01 2022 using A230097, verified with exhaustive search Oct 02 2022

a(9)-a(10) from Hugo Pfoertner, Nov 30 2022